Three-dimensional perceptions in haptic systems

ABSTRACT

An acoustic field may be produced from a transducer array having known relative positions and orientations. In this acoustic field, one or more control points may be defined. An amplitude may be assigned to the control point. Mid-air haptic effect for a virtual object on a human body part may be generated by moving the control point in a single closed curve comprising a plurality of curve segments. The single closed curve traverses at least one location where the human body part intersects with the virtual object. Additionally, a user may interact with virtual three-dimensional content using the user&#39;s hands while a tracking system monitoring the user&#39;s hands, a physics engine updates the properties of the virtual three-dimensional content and a haptic feedback system provides haptic information to the user.

RELATED APPLICATION

This application claims the benefit of the following four U.S.Provisional Patent Applications, all of which are incorporated byreference in their entirety:

1) Ser. No. 62/370,522, filed on Aug. 3, 2016;

2) Ser. No. 62/370,786, filed on Aug. 4, 2016;

3) Ser. No. 62/370,865, filed on Aug. 4, 2016; and

4) Ser. No. 62/397,419, filed on Sep. 21, 2016.

FIELD OF THE DISCLOSURE

The present disclosure relates generally to improved techniques forperception of simulated three-dimensional objects and generation ofthree-dimensional sound in haptic-based systems.

BACKGROUND

A continuous distribution of sound energy, referred to as an “acousticfield” may be used for a range of applications including haptic feedbackin mid-air. Such an acoustic field may be produced from a transducerarray having known relative positions and orientations. In this acousticfield, one or more control points may be defined. Such control pointsmay have a known spatial relationship relative to the transducer array.

These control points may be assigned an amplitude and thenamplitude-modulated with a signal and as a result produce vibro-tactilefeedback in mid-air. An alternative method to produce feedback is tocreate control points that are not modulated in amplitude and move themaround spatially to create “spatio-temporal” modulation that can befelt.

These control points are effectively concentrations of ultrasonicenergy, and moving them around generates disturbances in the air. Byspatially modulating these disturbances created by ultrasonic foci,simply moving them backwards and forwards, it is possible to generatelow frequency sound through the principle of acoustic radiation force asthe focus pushes on the air or other materials around it.

Furthermore, very sudden disturbances are created when such focus pointsare quickly created or destroyed without slowly increasing or decreasingthe amplitude. This creates pops or clicks which are often an unwantedside effect. Moving the control point can be used to achieve similareffects to changing the amplitude, but without the sharp changes inpressure that cause pops and clicks. This means that moving the controlpoint is much more preferable than changing its amplitude. Due to thespeed of sound being generally faster than the control point motion,this enables any generated pressure imbalances to dissipate, so thecontrol point may be moved quickly without creating powerful airdisturbances.

When considering the intersections between human hands and virtualobjects, each finger and the palm in many instances feel a very smallpart of the overall shape that go towards the appreciation of the whole.Thus, when the hand feels a small part of the shape intersection thewhole shape intersection must be created in order to not create anddestroy the necessary control points. If the control points were createdand destroyed such that they provide only the small part of theintersection, this would create unwanted noise. A more economical methodof describing a shape therefore would save power and time and would thenenable more of the power expended by the device to be used in creatinghaptic feedback in places which are touched by a hand.

Due to cross-modal and other perceptual effects, the induction of touchsensations through mid-air haptics remains surprisingly effective atcommunicating the existence, geometry and surface properties of objects.Fundamentally, although much research concentrates on explorationthrough touch alone, the effective use of these system is primarily usedand driven through systems that cross multiple sensory modalities toprovide an experience. For this reason, there exist in practice simplebut conceptually complicated effects that can only be achieved throughthe realization of these underlying principles.

Furthermore, with mid-air haptic devices, virtual objects may betheoretically recreated in mid-air for the user to touch. But due to thenature of mid-air feedback, some fundamental physical limitations exist.This is because there are some parts of the somatosensory system thatcannot be directly manipulated by the device, for examplethermoreceptors for temperature sensing. But finding an optimal methodto map output from the device—which necessarily has strengths andweaknesses peculiar to mid-air haptics—onto simulated physicalinteractions with virtual objects has been difficult. It is thereforevaluable to develop an approach that is readily accepted by a human ascorresponding to a plausible interaction with the object. Similarly, itis useful to manipulate focus point spinning in the air to generate asound wave each time it moves along a path.

BRIEF DESCRIPTION OF THE FIGURES

The accompanying figures, where like reference numerals refer toidentical or functionally similar elements throughout the separateviews, together with the detailed description below, are incorporated inand form part of the specification, and serve to further illustrateembodiments of concepts that include the claimed invention, and explainvarious principles and advantages of those embodiments.

FIG. 1 is a representation of a hand interacting with a virtual cube inaccordance with some embodiments.

FIG. 2 is a representation of a control point moving in air thatgenerates sound waves in accordance with some embodiments.

Skilled artisans will appreciate that elements in the figures areillustrated for simplicity and clarity and have not necessarily beendrawn to scale. For example, the dimensions of some of the elements inthe figures may be exaggerated relative to other elements to help toimprove understanding of embodiments of the present invention.

The apparatus and method components have been represented whereappropriate by conventional symbols in the drawings, showing only thosespecific details that are pertinent to understanding the embodiments ofthe present invention so as not to obscure the disclosure with detailsthat will be readily apparent to those of ordinary skill in the arthaving the benefit of the description herein.

DETAILED DESCRIPTION

The solution described herein involving touch and aural interactionswith virtual objects has properties that may be used in combination orseparately.

I. CURVE MANIPULATION FOR 3D-SHAPE REPRODUCTION

When a hand intersects the shell of a three dimensional simulated shape,the current solution is to find a closed curve that best represents theintersection that is to be described to the user and actuate that path.Since it is a closed path, the system may use a single control pointmoving along the path with a given speed (and thus frequency) in orderto produce it in mid-air haptics without much noise being created. Butthis suffers from two important limitations. First, only shapescontaining paths that can be conveniently interpreted as closed curvedcontours may be represented. A shape containing open contours is not assuitable for haptic representation although the path can be bent backupon itself, this changes the haptic effect. Second, if the constraintof a single control point is imposed (since each control point requirescomputation, it is prudent to use them sparingly) only one contour maybe used. If one contour is effective at providing feedback for onefinger and another contour is effective for the palm, both cannot beused without recourse to multiple control points, which would split thecapacity for output from a given device to provide multiple points offeedback. These drawbacks are in addition to the power limitations ofthe single contour approach. As the length of the contour increases, thespeed that the point moves increases the point become spread morethinly, eventually decreasing its effective haptic response.

Instead of taking a single contour, finding the set of all intersectionswith the parts of the user on which the haptic effect is to be elicited,as line or curve segments or surfaces is the best solution. But thiswould involve creating many open curves, and thus entail creating anddestroying the point many times at each beginning and end pointrespectively. Alternatively, this would require using many controlpoints in order to create separate haptic effects for each intersectionso that each region of haptic feedback may stay spatially locked. Forexample, in the specific case of a hand intersection, each finger andpotentially also the palm must have separate haptic effects. Thisrequires many points of contact, but so that the each control point maystay local to the point of contact or intersection, the existingsolution is either loud (creation and destruction of a single point) orcostly in device power and compute (many points). To overcome thisrequirement for multiple disconnected paths, taking the set of allintersections and then optimizing for the single shortest path thattraverses each of them is much more effective. But this action will moveacross the shape in a linear fashion with a beginning and an end, whichwill create a control point at the beginning, traverse the shape anddestroy the control point at the end, before recreating it at thebeginning of the shape. This continuous creation and destruction,although an improvement, remains incompatible with a quiet system.

By connecting the beginning and end of the curves into a single closedcurve and traversing it at the appropriate speed the desired hapticeffect can be generated with significantly reduced noise. Further, thisdoes not preclude amplitude modulation of the points as they traversethe given curves. This path is illustrated in FIG. 1.

Shown in FIG. 1 is a model 100 of a hand 110 interacting with ahaptically generated virtual object 120. The points 132, 134, 136, 138where the hand touches the virtual shape are connected into a path 140,and this path 140 is actuated, creating the feeling while moving thefocus smoothly. Smooth movement of the focus along the path 140 withoutinterruption minimizes any unwanted audible noise, resulting in correct,strong haptic sensation across multiple fingers while operating quietly.In addition, although FIG. 1 shows a hand 110, any body part may beused.

Because the curve connects each curve segment, the system determineswhether to traverse them in a preset clockwise or counterclockwisemotion. This motion is relative to a normal vector which may be definedrelative to the user (such as a local coordinate space relative to thegeometry of their hand), intersections or the geometry. Alternatively,it may be useful to use points traversing multiple curves in order toprovide feedback for more than one user or hand.

One drawback of this approach is that in order to close the curve theuser himself/herself must be avoided, in order to prevent spurioushaptic effects being created on the user at locations whereintersections did not occur. To achieve this in the context of theusers' hand, the curve should be either made to go over or under thehand (and thus defocusing at the location of the hand) or around thehand. Alternatively, the state space of the transducers may beinterpolated between each endpoint, removing the need to find aspatially coherent approach to closing the curve. The state of theultrasonic waves in the acoustic field is driven linearly by the complexvalued activation coefficients of each transducer. This requires,grouping all of these complex values for all transducers into ahigh-dimensional phase space and linearly interpolating between a firststate in the space (that represents, for instance, an end point on onecurve) and a second state (that represents an initial point at adifferent location). The linear interpolation must also apply to theacoustic fields resulting from the actuation of the newly created statesin the intermediate stages. It should be noted that in theseintermediate stages between the two states, the control point does notnecessarily have any particular location. But because the linearinterpolation applies to the produced acoustic field, the field mustsmoothly vary in time and therefore also could serve to also greatlyreduce audible output while achieving the movement between points.

Another potentially more compatible approach is to change the speed atwhich the control point is moving along the curve. To start, thesolution computes the length of the curve required to complete theclosed path, traversing each intersection curve segment in turn creatinghaptic effects at each intersection with the user. Next, firstconsidering only the parts of the path that do not contribute to thehaptic effects, the solution traverses these haptically unnecessarycurves at the fastest possible speed to avoid wasting power on them.This reduces the haptic actuation of these curves and is beneficial intwo ways. First, the amount of time taken to traverse these parts of thepath is reduced; second, if the user is intersected in error during thistime the amount of haptic effect that he/she would receive would beminimal. Nevertheless, in the limit of this technique, it will behave ascreation and destruction of the control point, creating pops and clicksas before. For this reason, it is useful to consider a speed limit thatlessens the effects generated by discontinuities between the states ofthe acoustic field. The result of this technique is to create a controlpoint that accelerates and decelerates between haptic regions. Byconsidering a curve harboring haptic effects in this way, there may bethe requirement that the curve must cycle at a haptically activefrequency. This has the effect of creating a time “budget” of a closedpath cycle period, part of which may be spent on the haptically activeparts of the path and the remainder used to reduce audible noise. Inthis light, the remaining time in the haptically-actuated curve lengthis split between the parts of the path that require haptics. This time“budget” must ensure that these intersections receive as much of theenergy from the array as possible so that haptic effects have the time(and thus power) to be realized at the intersections with the user. Inthis way, the device may be quiet and behave in a fashion that maximizesthe energy deposited on the parts of the user to be haptically actuatedsuch as the fingers.

Another issue is that the virtual shape or user position may dynamicallychange while haptic effects are being produced. For example, at thecurrent time t₀ a closed curve containing haptic effects is in currentuse. At the next time step in the future t₁, a new curve containinghaptic effects is synthesized to reflect the changes in the virtualshape. In this case, a further curve must be plotted that allows thepoint to traverse from the old curve representing the state of thevirtual and physical world at time t₀ to the new curve representing thestate at time t₁ without discontinuity. Selecting the closest point oneach curve, and constructing a path between them that allows the pointto move from the t₀ curve to the t₁ curve may be used to achieve this.This may also benefit from the introduction of a speed limit similarlyto the unactuated portion of the haptic path described previously tolimit the unusable traversal time from one curve to the other.

II. TOUCHING VIRTUAL THREE-DIMENSIONAL OBJECTS

A. Introduction

This disclosure is related to a system where a user interacts withvirtual 3D-content by a tracking system monitoring his/her hands, usinga physics engine to update the position and properties of the virtualcontent, and a haptic feedback system providing haptic information tothe user. The haptic system may be mid-air haptic feedback. A hapticimpulse may be applied to the user when his or her hand contacts avirtual object. This impulse may be applied at the exact location of thecontact. Or the user's hand is formed into a skeletal model and theimpulse is applied to each bone in the skeleton that contacts theobject.

The strength and duration of the impulse is adjusted based on outputfrom the physics engine, including momentum and physical properties ofthe hand and virtual object. The waveform of the haptic impulse may beadjusted based on the above physics engine outputs. A weaker hapticsensation may be applied to parts of the hand when the object isreleased or when contact with it ceases. In contrast, there is no hapticfeedback applied during continuous holding.

Haptic feedback may be applied to the opposite side of the hand to whichthe contact is occurring. And haptic feedback follows the hand for thedecaying amplitude experienced after contact.

B. Interacting with 3D Objects

A system may have a user who interacts with virtual 3D-content by atracking system monitoring his/her hands, using a physics engine toupdate the position and properties of the virtual content, and a hapticfeedback system providing haptic information to the user. The hapticsystem may use mid-air haptic feedback. A haptic impulse may be appliedto the user when his or her hand contacts a virtual object. This impulsemay be applied at the exact location of the contact. The user's hand maybe formed into a skeletal model and the impulse is applied to each bonein the skeleton that contacts the object. The strength and duration ofthe impulse may be adjusted based on output from the physics engine,including momentum and physical properties of the hand and virtualobject. The waveform of the haptic impulse may be adjusted based on theabove physics engine outputs.

A weaker haptic sensation may be applied to parts of the hand when theobject is release or when contact with it ceases. Furthermore, there maybe no haptic feedback applied during continuous holding. Haptic feedbackmay be applied to the opposite side of the hand to which the contact isoccurring. In addition, haptic feedback follows the hand for thedecaying amplitude experienced after contact.

Specifically, when a user is engaged in virtual reality that has beenenhanced by the addition of a mid-air haptic device, a hand trackingsystem may be employed to track their hands in order to determine theposition and orientation of each hand, finger and joint. Thisinformation can be input into the virtual world in the form of a virtualhand object that is capable of interactions with virtual objects, albeitonly one way. This is because the physical hand has one-to-onecorrespondence with, and puppets, the virtual hand. The virtual hand hasthe ability to interact with virtual objects, generally through someform of physics engine. (A physics engine is understood as one of thecomponents of a game engine.)

For rigid bodies that do not change shape, a physics engine willgenerally be responsible for managing the simulated forces and torquesapplied to the objects in the virtual world and the resulting changes inlinear, and angular, velocity and acceleration, before generating thecorresponding changes in spatial transformation for each object orobject part represented. Other object types may imply additionalmanagement or information, and may also include more complex simulationof physical phenomena.

Nonetheless, fundamentally, interactions between virtual objects aremediated by their simulated forces and torques, which must be foundbefore these interactions can be simulated. In order to find thesesimulated forces and torques, the physics engine will ensure virtualobjects are tested for “collisions”, which is effectively testing forfuture situations in which objects in the virtual scene might intersect.This generates collision information which feeds the management portionof the physics engine with positions, velocities, forces and torques.This information can also be used to inform a haptics engine about whata user might feel if parts of the user extended into the virtual world.But this machine is unable to affect the physical user due to thevirtual objects not being able to physically collide with the user. Inthe case of the users' hand, the virtual objects do not affect thevirtual hand and thus physical hand. This disconnect causes a loss ofimmersion in the virtual world.

A satisfying experience results if the mid-air haptic device isconfigured to provide feedback to the user at the point at which animpulse (a short sharp force, during which the force changes in timesharply), contact or similar interaction in which the force changessharply in time is applied to the virtual object by the user, or on thevirtual representation of the user by the virtual object. A hapticimpulse that mirrors this may be created by generating a similarly shorthaptic effect. This is effective because of the occurrence of anillusion of two-way interaction due to the cross-modal effects in playat this setting. This haptic impulse may then be adjusted using thetrajectory of the object and the hand, along with the simulatedmomentum, restitution and other physical properties of the object andhand.

The feedback may then be applied with an intensity and waveformappropriate and proportional to the impulse applied. Due to theproprioceptive and cross-modal phenomena in effect in this situation, inthe case of the users' hand, the closest addressable part of the handmay be used (including through the hand). The user will still perceivethis haptic effect to be originating at the location of the collision.Thus, if the impulse occurs on the back of the hand, due to the relativevibrotactile receptiveness of glabrous skin on the opposite side of thehand, this other side would be actuated instead of the real location ofthe contact. Perceptual effects then cause the user to believe that theimpulse was stimulated in the correct location.

In addition, the user in a virtual world may want to pick up virtualobjects. Since picking up and dropping objects is a common activity, itis important to preserve the user experience through this process. Whenpicking up an object, the user receives impulses corresponding to thegrip placed on the object. During the grip time, no feedback is applied.When the object is released or dropped from the users' virtual grip, areduced impulse is used to indicate that the object has been released.

In many cases, the feedback follows the part of the hand to which theimpulse was directed since it is modelling the vibration of andsubsequent haptic effect on the skin at the point of contact. Thefeeling on contact can be accentuated, potentially using a decayingamplitude on the point of contact on the hand, to create a morepersuasive effect and overcome the short duration of each impulse. Theduration of the impulse may also be driven by data from the physicsengine.

III. SPATIO-TEMPORALLY MODULATED SOUND

A. Sound from Ultrasound Via an Alternate Mechanism

The noise generated from certain haptic-based interactions is often anunwanted side effect of the haptic activity. But it is possible to usethe property of noise generation to produce desired sound effects.Precisely controlling disturbances in haptic systems that generate lowfrequency noise provides the capacity to generate broadband signals byspatially moving the focusing points. This enables the creation of soundfrom ultrasound using an entirely different mechanism from existingparametric audio applications. Rather than modulating a point or beam inamplitude, a control point may instead be moved in a trajectory thatencodes the waveform. This turns the control point into an audio source.

B. Plotting Spatial Trajectories

Turning to FIG. 2, shown is a representation 200 of a focus point 210spinning in the air via, path 220, which generates a sound wave 230 eachtime it moves along the path 220. The motion can be modified toreproduce a sound that is audible to the human ear in a localized waywithout amplitude modulating the focusing system.

The easiest way to generate these trajectories is to take an existingsound source and reinterpret it as a linear path along which a focuspoint moves to create a sound wave. At each point in time, the level ina digitally sampled sound channel may be interpreted as a parameterizedposition along this path that the focus is to be created. By creatingfoci at these positions at the sampled time offsets, an audible soundcan be created along a 1D open curve path.

Alternatively, such an existing digitally sampled sound source may bedecomposed into in-phase and quadrature components, that is into thereal and imaginary parts of a complex signal that describes the audio.This is not trivial for an audio source since it is wideband. Thus, themost effective way to achieve the desired result is to apply a Fouriertransform to the signal and apply a π/2 phase offset. The standardapproaches concerning windowing, blocking of the signal and transitionsin phase may also be used. This generates the imaginary component of thesampled audio signal. Since the signal may be represented as a complexvalue, the signal may be mapped onto a 1D closed curve, or a 2D circle,plane or surface. Moving the point around or remapping these 2Dcoordinates into the space will produce sound waves, thereby recreatingthis audio signal. In this way, the audio signal may be generated in a2D area.

This effect may also be used in a third dimension to provide the phasecues that govern stereo audio (potentially with a single sound source)for systems that cannot create strong foci in disparate positions.Similarly, for multiple focus points, multiple sound sources may besynthesized. This enables multi-channel audio that can be created fromfocus points in the air. These focus points may also provide hapticfeedback.

IV. GENERATIVE HAPTICS FROM AUDIO EXEMPLARS

Control points may be changed in amplitude many thousands of times asecond, although only low frequencies can be detected as haptics.Through non-linearity effects, higher frequencies can be reproduced.Updating the control points quickly yields the ability to produce manyfrequencies at once, giving the ability to reproduce audio in somesense. However, audio does not have information in frequency ranges thatare haptically effective.

Designing haptic effects in the air is challenging as due to thesensitivity of the skin only some bands of frequencies are available forhaptic use. Due to this, effects can be created that create pleasurablesounds from the array that do not convey haptics and conversely hapticeffects that do not sound pleasing. Due to these reasons, an easierapproach to designing mid-air haptic effects would be valuable.

Creating a haptic sensation using a sound as input may be achieved in anumber of ways. The frequencies of the sound that are in the hapticrange may be amplified until a haptic threshold is reached.Alternatively, the initial sound may have frequencies that arehaptically active added to it. The original sound may be analyzed and aprofile constructed. This profile may then be used to generate a hapticeffect. This may be constructed using the qualities present in thesound, allowing the created haptic texture to take on aspects of theexemplar such as speed, rhythm or texture. The sound may be processedinto a haptic effect using a variety of processing mechanisms. Thesemechanisms may be configured to emphasize certain aspects in theresultant haptic effect while potentially ignoring others. This can alsobe achieved by extracting a feature set from the sound before processingthe sound into a haptic effect. A feature set could also containdiscontinuities inferred from the sound, such as for example a plosivephoneme being interpreted in this way.

Specifically, this can be implemented by (1) extracting a feature setfrom a sound profile before assigning the plurality of amplitudes to thecontrol point over a preset time period; and (2) applying a feature setto the plurality of amplitudes assigned to the control point over apreset time period. Alternatively, it can implemented by (1) extractinga feature set from the plurality of amplitudes to the control point overa preset time period; and (2) applying the feature set to the soundprofile.

A library of haptic effects may be searched and sorted based on theextracted feature set alongside similarity metrics in order to providefeedback to a haptic author. This haptic author may use the soundinterface to describe basic components of a haptic effect, which canthen be edited and mixed further. The haptic effect may also be mixedback into the waveform, resulting in a combination of audio and hapticeffects. This may occur automatically or via a range of processingstyles. These may involve accentuating or augmenting particular hapticeffects in order to stylize the effects. The processing styles may beconcatenated or remixed to create new processing schemes. Labels can beattached to these processing mechanisms and haptic effects, such as“buzzy” or “warm”. These may be used to adjust existing haptic effects,adjust audio inputs to be synthesized into haptic effects or search forexisting effects that are examples of the style described.

V. CONCLUSION

The various features of the foregoing embodiments may be selected andcombined to produce numerous variations of improved haptic systems.

In the foregoing specification, specific embodiments have beendescribed. However, one of ordinary skill in the art appreciates thatvarious modifications and changes can be made without departing from thescope of the invention as set forth in the claims below. Accordingly,the specification and figures are to be regarded in an illustrativerather than a restrictive sense, and all such modifications are intendedto be included within the scope of present teachings.

The benefits, advantages, solutions to problems, and any element(s) thatmay cause any benefit, advantage, or solution to occur or become morepronounced are not to be construed as a critical, required, or essentialfeatures or elements of any or all the claims. The invention is definedsolely by the appended claims including any amendments made during thependency of this application and all equivalents of those claims asissued.

Moreover, in this document, relational terms such as first and second,top and bottom, and the like may be used solely to distinguish oneentity or action from another entity or action without necessarilyrequiring or implying any actual such relationship or order between suchentities or actions. The terms “comprises,” “comprising,” “has”,“having,” “includes”, “including,” “contains”, “containing” or any othervariation thereof, are intended to cover a non-exclusive inclusion, suchthat a process, method, article, or apparatus that comprises, has,includes, contains a list of elements does not include only thoseelements but may include other elements not expressly listed or inherentto such process, method, article, or apparatus. An element proceeded by“comprises . . . a”, “has . . . a”, “includes . . . a”, “contains . . .a” does not, without more constraints, preclude the existence ofadditional identical elements in the process, method, article, orapparatus that comprises, has, includes, contains the element. The terms“a” and “an” are defined as one or more unless explicitly statedotherwise herein. The terms “substantially”, “essentially”,“approximately”, “about” or any other version thereof, are defined asbeing close to as understood by one of ordinary skill in the art. Theterm “coupled” as used herein is defined as connected, although notnecessarily directly and not necessarily mechanically. A device orstructure that is “configured” in a certain way is configured in atleast that way, but may also be configured in ways that are not listed.

The Abstract of the Disclosure is provided to allow the reader toquickly ascertain the nature of the technical disclosure. It issubmitted with the understanding that it will not be used to interpretor limit the scope or meaning of the claims. In addition, in theforegoing Detailed Description, it can be seen that various features aregrouped together in various embodiments for the purpose of streamliningthe disclosure. This method of disclosure is not to be interpreted asreflecting an intention that the claimed embodiments require morefeatures than are expressly recited in each claim. Rather, as thefollowing claims reflect, inventive subject matter lies in less than allfeatures of a single disclosed embodiment. Thus the following claims arehereby incorporated into the Detailed Description, with each claimstanding on its own as a separately claimed subject matter.

The invention claimed is:
 1. A method comprising: producing an acousticfield from a transducer array having known relative positions andorientations; defining a control point wherein the control point has aknown spatial relationship relative to the transducer array; assigningan amplitude to the control point; generating a mid-air haptic effectfor a user by traversing the control point in a closed curve usingsmooth movement without interruption to minimize unwanted audible noise,wherein the single closed curve comprises a plurality of curve segments.2. The method as in claim 1, wherein the closed curve is traversedrelative to a normal vector defined relative to the user.
 3. The methodas in claim 1, wherein the closed curve comprises multiple curves toprovide feedback to multiple users.
 4. The method as in claim 1, whereinthe closed curve is defocused at a user's location.
 5. The method as inclaim 1, wherein traversing the control point in a single closed curvecomprises: computing a length of the closed curve required to complete aclosed path; for each of the plurality of curve segments, creatingadditional haptic effects at each intersection with a user; for theplurality of curve segments that do not contribute to the hapticeffects, traversing the control point at a faster speed.